Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}4x+y &= 1 \\ 5x-7y &= 2\end{align*}$
Answer: Begin by moving the $x$ -term in the second equation to the right side of the equation. $-7y = -5x+2$ Divide both sides by $-7$ to isolate $y$ $y = {\dfrac{5}{7}x - \dfrac{2}{7}}$ Substitute this expression for $y$ in the first equation. $4x+({\dfrac{5}{7}x - \dfrac{2}{7}}) = 1$ $4x + \dfrac{5}{7}x - \dfrac{2}{7} = 1$ Simplify by combining terms, then solve for $x$ $\dfrac{33}{7}x - \dfrac{2}{7} = 1$ $\dfrac{33}{7}x = \dfrac{9}{7}$ $x = \dfrac{3}{11}$ Substitute $\dfrac{3}{11}$ for $x$ back into the top equation. $4( \dfrac{3}{11})+y = 1$ $\dfrac{12}{11}+y = 1$ $y = -\dfrac{1}{11}$ $y = -\dfrac{1}{11}$ The solution is $\enspace x = \dfrac{3}{11}, \enspace y = -\dfrac{1}{11}$.